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Midland Park Public Schools
6th Grade Mathematics
Course Description: The curriculum in the 6th grade mathematics is aligned with the New Jersey Student Learning Standards.
Those standards focus on following five areas: ratios and proportional relationships, the number system,
equations and expressions, geometry, and statistics and probability. Students will develop their ability to make
sense of problems and persevere in solving them, reason abstractly, construct arguments and critique others,
model mathematically, attend to precision, and use repeated reasoning. Students will demonstrate
understanding of the course material by participating in homework, group and individual class work, quizzes,
tests, independent problem solving and Do Now’s.
Course Sequence:
Unit Title Pacing
Unit 1: The Number System 44 days
Unit 2: Expressions and Equations 43 days
Unit 3: Rates and Ratios 33 days
Unit 4: Geometry 26 days
Unit 5: Statistics and Probability 25 days
*9 days built in for field trips, class parties, state testing, and end of year promotion activities.
Pre-requisite: 5th grade math
Midland Park Public Schools
Unit 1 - Overview Content Area: Mathematics
Unit Title: Unit 1: The Number System
Grade Level: 6th
Unit Summary
● Whole Number Operations ● Fractions ● Decimals
Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems.
Unit 1 - Standards
Standards (Content and Technology):
CPI#: Statement:
6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.
6.NS.B.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common
multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum
of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with
no common factor. For example, express 36 + 8 as 4 (9 + 2).
6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by
fractions, e.g., by using visual fraction models and equations to represent the problem. For example,
create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the
relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is
2/3. (In general, (a/b) ÷ (c/d) = ad/bc). How much chocolate will each person get if 3 people share 1/2 lb
of chocolate equally? How many 3/4- cup servings are in 2/3 of a cup of yogurt? How wide is a
rectangular strip of land with length 3/4 mi and area 1/2 square mi?
6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each
operation.
21st century themes and skills (standard 9)
9.1.8.E.1 Explain what it means to be a responsible consumer and the factors to consider when making consumer
decisions.
Career Ready Practices
CRP1 Act as a responsible and contributing citizen and employee.
CRP2 Apply appropriate academic and technical skills.
CRP4 Communicate clearly and effectively and with reason.
CRP8 Utilize critical thinking to make sense of problems and persevere in solving them.
Educational Technology Standards
8.1.8.A.1 Demonstrate knowledge of a real world problem using digital tools.
8.1.8.A.3 Use and/or develop a simulation that provides an environment to solve a real world problem or theory.
Interdisciplinary Connection
SL.6.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with
diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and expressing their own
clearly.
SL.6.2 Interpret information presented in diverse media and formats (e.g., visually, quantitatively, orally) and
explain how it contributes to a topic, text, or issue under study.
NJSLSA.L2 Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling
when writing.
Unit Essential Question(s):
How do you divide multi-digit numbers?
How do you multiply multi-digit numbers?
How do you write the prime factorization of a
number?
Unit Enduring Understandings:
Estimation is a very useful mathematical
tool.
It is important to extend knowledge from
whole numbers to rational numbers in order
Midland Park Public Schools
How can you find the least common multiple of two
whole numbers?
How can you find the greatest common factor of two
whole numbers?
How can you compare and order fractions and
decimals?
How do you multiply fractions?
How do you divide fractions?
How do you add and subtract multi-digit decimals?
How do you multiply multi-digit decimals?
How do you divide decimals by whole numbers?
How do you divide whole numbers and decimals by
decimals?
to fully understand and solve real world
problems.
Unit Learning Targets/Objectives:
Students will be able to...
Fluently divide multi-digit numbers using the standard algorithm.
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple
of two whole numbers less than or equal to 12.
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions
Evidence of Learning
Formative Assessments: Teacher observations, exit slips, homework, participation, communicator white boards
Summative/Benchmark Assessment(s): Lesson quizzes, Unit Test
Alternative Assessments: Modified versions of quizzes and tests
Resources/Materials : Smart Board, curriculum folders, scope and sequence calendar, math textbook, math
manipulatives. Online resources such as IXL, xtramath, Think Central, etc
Modifications:
● Special Education Student/504 ‐ Allow errors, Rephrase
questions, directions, and explanations, Allow use of
calculator and extended time on assignments. Consult
IEP/504 for specific modifications/accommodations.
● English Language Learners ‐ Allow errors in speaking,
rephrase questions, directions, and explanations,
extended time on assignments.
● At-Risk Students - Consult with Guidance
Counselors and follow I&RS procedures/action
plans, extra help, breaking down tasks.
● Gifted and Talented Students – Make Peer Leaders,
provide extension activities.
Suggested Pacing Guide Lesson
Name/Topic Lesson Objective(s)
Students will... Time frame (day(s) to complete)
Benchmark
Testing
2 days
Multiply Multi
Digit Numbers
Multiply multi digit numbers. 1 day
Divide multi digit
numbers
Divide multi digit numbers. 1 day
Exponents Evaluate expressions involving
exponents.
2 days
Assessment Demonstrate skills above 1 day
Order of
Operations
Use the order of operations to evaluate
expressions involving exponents.
3 days
Prime
Factorization
Write the prime factorization of
numbers.
1 day
Greatest
Common Factor
Find the greatest common factor of two
whole numbers.
2 days
Midland Park Public Schools
Least Common
Multiple
Find the least common multiple of two
whole numbers.
2 days
Assessment Demonstrate skills above 1 day
Compare and
Order Fractions
Compare and Order Fractions 3 days
Adding Fractions Add fractions using a common
denominator
1 day
Subtracting
Fractions
Subtract fractions using a common
denominator
1 day
Multiply
Fractions
Multiply fractions. 1 day
Divide Fractions Divide proper fractions and mixed
numbers using a common denominator.
3 days
Assessment Demonstrate skills above 1 day
Order of
Operations with
fractions
Use the order of operations to evaluate
expressions involving fractions
2 days
Unit Test Demonstrate skills above 2 days
Compare and
Order Decimals
Compare and order decimals 2 days
Add and subtract
decimals
Add and subtract decimals 1 day
Multiply
decimals
Fluently multiply multi digit decimals 1 day
Assessment Demonstrate skills above 1 day
Dividing
Decimals
Divide decimals by decimals and
decimals by whole numbers
2 days
Order of
Operations with
Decimals
Use the order of operations to evaluate
expressions involving decimals
2 days
Assessment Demonstrate skills above 1 day
Teacher Notes: Students will use prior knowledge by using the ‘cake method’ for LCM and GCF. Students will be
shown 6 ways to compare fractions. Students should use a common denominator to add, subtract and multiply fractions.
Students should use the ‘moth method’ to simplify fractions before multiplying them. Use brownie pans to multiply
proper fractions. Use of fraction tiles to compare and order fractions.
Additional Resources:
https://www.ixl.com/ https://www.khanacademy.org/
https://xtramath.org
https://www-k6.thinkcentral.com/ePC/start.do
Midland Park Public Schools
Unit 2 - Overview Content Area: Mathematics
Unit Title: Unit 2: Expressions and Equations
Grade Level: 6th
Unit Summary
● Algebraic Expressions ● Algebraic Equations and Inequalities ● Integers and the Coordinate Plane
Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities.
Unit 2 - Standards
Standards (Content and Technology):
CPI#: Statement:
6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents.
6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.A.3 Apply the properties of operations to generate equivalent expressions. For example, apply the
distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the
distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply
properties of operations to y + y + y to produce the equivalent expression 3y.
6.EE.A.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number
regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are
equivalent because they name the same number regardless of which number y stands for.
6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a
specified set, if any, make the equation or inequality true? Use substitution to determine whether a given
number in a specified set makes an equation or inequality true.
6.EE.B.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical
problem; understand that a variable can represent an unknown number, or, depending on the purpose at
hand, any number in a specified set.
6.EE.B.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and
px = q for cases in which p, q and x are all nonnegative rational numbers.
6.EE.B.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or
mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many
solutions; represent solutions of such inequalities on number line diagrams.
6.EE.C.9 Use variables to represent two quantities in a real-world problem that change in relationship to one
another; write an equation to express one quantity, thought of as the dependent variable, in terms of the
other quantity, thought of as the independent variable. Analyze the relationship between the dependent
and independent variables using graphs and tables, and relate these to the equation. For example, in a
problem involving motion at constant speed, list and graph ordered pairs of distances and times, and
write the equation d = 65t to represent the relationship between distance and time
6.NS.C.6 Understand a rational number as a point on the number line. Extend number line diagrams and
coordinate axes familiar from previous grades to represent points on the line and in the plane with
negative number coordinates.
6.NS.C.7 Understand ordering and absolute value of rational numbers.
21st century themes and skills (standard 9)
9.1.4.C.1 Explain why people borrow money and the relationship between credit and debt.
9.1.8.E.1 Explain what it means to be a responsible consumer and the factors to consider when making consumer
decisions.
Career Ready Practices
CRP1 Act as a responsible and contributing citizen and employee.
Midland Park Public Schools
CRP2 Apply appropriate academic and technical skills.
CRP4 Communicate clearly and effectively and with reason.
CRP8 Utilize critical thinking to make sense of problems and persevere in solving them.
Educational Technology Standards
8.1.8.A.1 Demonstrate knowledge of a real world problem using digital tools.
8.1.8.A.3 Use and/or develop a simulation that provides an environment to solve a real world problem or theory.
Interdisciplinary Connection
SL.6.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-
led) with diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and
expressing their own clearly. SL.6.2 Interpret information presented in diverse media and formats (e.g., visually, quantitatively, orally) and
explain how it contributes to a topic, text, or issue under study.
NJSLSA.L4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases by using
context clues, analyzing meaningful word parts, and consulting general and specialized reference
materials, as appropriate.
Unit Essential Question(s):
How do you write and find the value of expressions involving
exponents?
How do you use the order of operations to evaluate expressions
involving exponents?
How do you write an algebraic expression to represent a situation?
How can you describe the parts of an expression?
How do you evaluate an algebraic expression or a formula?
How can you use variables and algebraic expressions to solve
problems?
How can you use the strategy use a model to combine like terms?
How can you use properties of operations to write equivalent
algebraic expressions?
How can you identify equivalent algebraic expressions?
How do you determine whether a number is a solution of an
equation?
How do you write an equation to represent a situation?
How do you solve addition and subtraction equations?
How do you solve multiplication and division equations?
How do you determine whether a number is a solution of an
inequality?
How do you write an inequality to represent a situation?
How can you write an equation to represent the relationship between
an independent variable and a dependent variable?
How can you translate between equations and tables?
How can you graph the relationship between two quantities?
How can you translate between equations and graphs?
Unit Enduring Understandings:
As students write equations to represent situations and solve equations to find solutions to problems, they will recognize that it is important to attend to precision.
Students learn to understand the relationships between variables by examining that relationship and abstracting the general rule from a table of values that relates the variables. This is one way they look for and express regularity in repeated reasoning.
Unit Learning Targets/Objectives:
Students will be able to...
Write and evaluate expressions involving exponents
Write algebraic expressions.
Evaluate algebraic expressions and formulas.
Use the properties of operations to generate equivalent algebraic expressions.
Identify equivalent algebraic expressions.
Determine whether a number is a solution of an equation.
Use algebra to solve addition and subtraction equations.
Use algebra to solve multiplication and division equations.
Midland Park Public Schools
Determine whether a number is a solution of an inequality.
Write algebraic inequalities.
Write an equation to represent the relationship between an independent variable and a dependent variable.
Compare and Order Integers.
Find and interpret the absolute value of integers.
Translate between equations and tables.
Graph the relationship between two quantities.
Translate between equations and graphs. Evidence of Learning
Formative Assessments: Teacher observations, exit slips, Do Nows, homework, participation, communicator
white boards
Summative/Benchmark Assessment(s): Lesson quizzes, Unit Test
Alternative Assessments: Modified versions of quizzes and tests
Resources/Materials : Smart Board, curriculum folders, scope and sequence calendar, math textbook, math
manipulatives. Online resources such as IXL, xtramath, Think Central, etc
Modifications:
● Special Education Student/504 ‐ Allow errors, Rephrase questions,
directions, and explanations, Allow use of calculator and extended time
on assignments. Consult IEP/504 for specific
modifications/accommodations. ● English Language Learners ‐ Allow errors in speaking, rephrase
questions, directions, and explanations, extended time on assignments.
● At-Risk Students - Consult with
Guidance Counselors and follow
I&RS procedures/action plans, extra
help, breaking down tasks. ● Gifted and Talented Students – Make
Peer Leaders, provide extension
activities. Suggested Pacing Guide
Lesson
Name/Topic Lesson Objective(s)
Students will... Time frame (day(s) to complete)
Intro to
expressions
Write and evaluate expressions involving
exponents
1 day
Expressions Write algebraic expressions. 2 days
Translating and
Writing
Expressions
Evaluate algebraic expressions and formulas. 3 days
Assessment Demonstrate skills above 1 day
Properties Use the properties of operations to generate
equivalent algebraic expressions.
3 days
Combine Like
Terms
Identify equivalent algebraic expressions. 2 days
Assessment Demonstrate skills above 1 day
Intro to
Equations
Determine whether a number is a solution of
an equation.
1 day
Addition and
Subtraction
Equations
Use algebra to solve addition and subtraction
equations.
2 days
Multiplication
and Division
Equations
Use algebra to solve multiplication and
division equations.
2 days
Mixed Practice Use algebra to solve addition, subtractions,
multiplication and division equations.
1 day
Assessment Demonstrate skills above 1 day
Intro to
Inequalities
Determine whether a number is a solution of
an inequality.
2 days
Inequalities Write algebraic inequalities. 2 days
Midland Park Public Schools
Inequality Word
Problems
Write and solve algebraic inequalities.
1 day
Assessment Demonstrate skills above 1 day
Rational
Numbers
Compare and Order Integers. 2 days
Absolute Value Find and interpret the absolute value of
integers.
2 days
Intro to the
Coordinate Plane
Translate between equations and tables. 3 days
Coordinate Plane Graph the relationship between two quantities. 3 days
Independent and
Dependent
Variables
Write an equation to represent the relationship
between an independent variable and a
dependent variable.
2 days
Graphing Linear
Equations
Translate between equations and graphs. 2 days
Assessment Demonstrate skills above 1 day
Teacher Notes: Use cups and chips to solve one step Algebraic equations. Use geoboards to locate points on the
coordinate plane and to graph linear equations.
Additional Resources:
https://www.ixl.com/ https://www.khanacademy.org/
https://xtramath.org
https://www-k6.thinkcentral.com/ePC/start.do
Midland Park Public Schools
Unit 3 - Overview Content Area: Mathematics
Unit Title: Unit 3: Ratios and Proportional Relationships
Grade Level: 6th
Unit Summary
● Rates, Ratios and Unit Rates ● Units of Measure ● Percents
Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates.
Unit 3 - Standards
Standards (Content and Technology):
CPI#: Statement:
6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two
quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for
every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly
three votes.”
6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in
the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of
sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a
rate of $5 per hamburger.”
6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about
tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
6.RP.A.3.a Make tables of equivalent ratios relating quantities with whole number measurements, find missing
values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
6.RP.A.3.b Solve unit rate problems including those involving unit pricing and constant speed. For example, if it
took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what
rate were lawns being mowed?
6.RP.A.3.c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity);
solve problems involving finding the whole, given a part and the percent.
6.RP.A.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when
multiplying or dividing quantities.
21st century themes and skills (standard 9)
9.1.8.E.6 Compare the value of goods or services from different sellers when purchasing large quantities and
small quantities.
9.1.4.E.2 Apply comparison shopping skills to purchasing decisions.
Career Ready Practices
CRP1 Act as a responsible and contributing citizen and employee.
CRP2 Apply appropriate academic and technical skills.
CRP4 Communicate clearly and effectively and with reason.
CRP8 Utilize critical thinking to make sense of problems and persevere in solving them.
Educational Technology Standards
8.1.8.A.1 Demonstrate knowledge of a real world problem using digital tools.
8.1.8.A.3 Use and/or develop a simulation that provides an environment to solve a real world problem or theory.
Interdisciplinary Connection
SL.6.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-
led) with diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and
expressing their own clearly. SL.6.2 Interpret information presented in diverse media and formats (e.g., visually, quantitatively, orally) and
explain how it contributes to a topic, text, or issue under study.
Unit Essential Question(s): Unit Enduring Understandings:
Midland Park Public Schools
How can you model ratios?
How do you write ratios and rates?
How can you use a multiplication table to find equivalent ratios?
How can you use tables to solve problems involving equivalent
ratios?
How can you use unit rates to make comparisons?
How can you solve problems using unit rates?
How can you use a graph to represent equivalent ratios?
How can you use ratio reasoning to convert from one unit of length
to another?
How can you use ratio reasoning to convert from one unit of
capacity to another?
How can you use ratio reasoning to convert from one unit of weight
or mass to another?
How can you transform units to solve problems?
How can you use the strategy use a formula to solve problems
involving distance, rate, and time?
How can you use a model to show a percent?
How can you write percents as fractions and decimals?
How can you write fractions and decimals as percents?
How do you find a percent of a quantity?
How can you find the whole given a part and the percent?
Working with ratios, rates, and
solving problems involving
equivalent ratios, provides
students many opportunities to
reason abstractly and
quantitatively.
Students should make sense of
problems and persevere in
solving them.
Percents help students see the
power of mathematics to model
and solve problems in their
everyday life.
Unit Learning Targets/Objectives:
Students will be able to...
Model ratios.
Write ratios and rates.
Use a multiplication table to find equivalent ratios.
Use tables to solve problems involving equivalent ratios.
Use unit rates to make comparisons.
Solve problems using unit rates.
Use a graph to represent equivalent ratios.
Use ratio reasoning to convert from one unit of length to another.
Use ratio reasoning to convert from one unit of capacity to another.
Use ratio reasoning to convert from one unit of weight mass to another.
Use a model to show a percent as a rate per 100.
Write percents as fractions and decimals.
Write fractions and decimals as percents.
Find a percent of a quantity.
Find the whole given a part and the percent. Evidence of Learning
Formative Assessments: Teacher observations, exit slips, homework, participation, communicator white boards
Summative/Benchmark Assessment(s): Lesson quizzes, Unit Test
Alternative Assessments: Modified versions of quizzes and tests
Resources/Materials : Smart Board, curriculum folders, scope and sequence calendar, math textbook, math
manipulatives. Online resources such as IXL, xtramath, Think Central, etc
Modifications:
● Special Education Student/504 ‐ Allow errors, Rephrase questions,
directions, and explanations, Allow use of calculator and extended time
on assignments. Consult IEP/504 for specific
modifications/accommodations.
● At-Risk Students - Consult with
Guidance Counselors and follow
I&RS procedures/action plans, extra
help, breaking down tasks.
Midland Park Public Schools
● English Language Learners ‐ Allow errors in speaking, rephrase
questions, directions, and explanations, extended time on assignments. ● Gifted and Talented Students – Make
Peer Leaders, provide extension
activities. ●
Suggested Pacing Guide Lesson
Name/Topic Lesson Objective(s)
Students will... Time frame (day(s) to complete)
Intro to Ratios Model ratios. 1 day
Ratios and Rate Write ratios and rates. 2 days
Unit Rate Use unit rates to make comparisons.
Solve problems using unit rates.
2 days
Equivalent Ratios Use a multiplication table to find equivalent ratios.
Use tables to solve problems involving equivalent ratios.
1 day
Graphing Ratios Use a graph to represent equivalent ratios. 1 day
Assessment Demonstrate skills above 1 day
Proportion Use tables to solve problems involving equivalent ratios. 3 days
Scale Drawings Use tables to solve problems involving equivalent ratios. 3 days
Intro to Linear
Measurements
Use ratio reasoning to convert from one unit of length to
another.
2 days
Units of Capacity Use ratio reasoning to convert from one unit of capacity
to another.
1 day
Units of Weight
and Mass
Use ratio reasoning to convert from one unit of weight
mass to another.
2 days
Assessment Demonstrate skills above 1 day
Intro to Percents Use a model to show a percent as a rate per 100.
Write percents as fractions and decimals.
Write fractions and decimals as percents.
2 days
Percents
multiples of 10
Find a percent of a quantity.
Find the whole given a part and the percent.
1 day
Percents
multiples of
20/25
Find a percent of a quantity.
Find the whole given a part and the percent.
1 day
All other percents Find a percent of a quantity.
Find the whole given a part and the percent.
1 day
Sales Tax and
Discount
Find a percent of a quantity.
Find the whole given a part and the percent.
2 days
Assessment Demonstrate skills above 1 day
Teacher Notes: Use half inch grid paper to discover and remember units of capacity. Use feet and yard stick for units of
measure. Cube lesson for intro to percents. Use percent bars for 10, 20 and 25%.
Additional Resources:
https://www.ixl.com/ https://www.khanacademy.org/
https://xtramath.org
https://www-k6.thinkcentral.com/ePC/start.do
Midland Park Public Schools
Unit 4 - Overview Content Area: Mathematics
Unit Title: Unit 4: Geometry
Grade Level: 6th
Unit Summary
● Area of two dimensional figures ● Surface area of two dimensional figures ● Volume of three dimensional figures
Students in build on their work with area by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Students find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths.
Unit 4 - Standards
Standards (Content and Technology):
CPI#: Statement:
6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into
rectangles or decomposing into triangles and other shapes; apply these techniques in the context of
solving real-world and mathematical problems.
6.G.A.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes
of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found
by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes
of right rectangular prisms with fractional edge lengths in the context of solving real-world and
mathematical problems.
6.G.A.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the
length of a side joining points with the same first coordinate or the same second coordinate. Apply these
techniques in the context of solving real-world and mathematical problems.
6.G.A.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to
find the surface area of these figures. Apply these techniques in the context of solving real-world and
mathematical problems.
21st century themes and skills (standard 9)
9.1.8.E.1 Explain what it means to be a responsible consumer and the factors to consider when making consumer
decisions.
Career Ready Practices
CRP1 Act as a responsible and contributing citizen and employee.
CRP2 Apply appropriate academic and technical skills.
CRP4 Communicate clearly and effectively and with reason.
CRP8 Utilize critical thinking to make sense of problems and persevere in solving them.
Educational Technology Standards
8.1.8.A.1 Demonstrate knowledge of a real world problem using digital tools.
8.1.8.A.3 Use and/or develop a simulation that provides an environment to solve a real world problem or theory.
Interdisciplinary Connection
SL.6.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-
led) with diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and
expressing their own clearly. SL.6.2 Interpret information presented in diverse media and formats (e.g., visually, quantitatively, orally) and
explain how it contributes to a topic, text, or issue under study.
NJSLSA.L2 Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling
when writing.
Midland Park Public Schools
Unit Essential Question(s):
How can you find the area of parallelograms?
What is the relationship among the areas of triangles,
rectangles, and parallelograms?
How can you find the area of triangles?
What is the relationship between the areas of
trapezoids and parallelograms?
How can you find the area of trapezoids?
How can you find the area of regular polygons?
How can you find the area of composite figures?
How can you plot polygons on a coordinate plane
and find their side lengths?
How do you use nets to represent three-dimensional
figures?
What is the relationship between a net and the
surface area of a prism?
How can you find the surface area of prisms?
How can you find the surface area of a pyramid?
How can you find volumes of rectangular prisms
with fractional edge lengths?
Unit Enduring Understandings:
Students reason abstractly and quantitatively
when they make sense of area formulas. They do
this by using their prior knowledge to derive
formulas and represent them symbolically. This
reasoning helps students to explain problems, the
problem-solving process, and justify their
solutions.
Modeling solid figures can help students make
sense of problems and persevere in solving them.
Filling spaces with cubes provides an image for
students to relate to the formula for the volume of
a rectangular prism. Knowing such strategies will
encourage students to persevere until they can
find a reasonable solution.
Unit Learning Targets/Objectives:
Students will be able to...
Find the area of parallelograms.
Find the area of triangles.
Find the area of trapezoids.
Find the area of regular polygons.
Find the area of composite figures.
Plot polygons on a coordinate plane, and use coordinates to find side lengths.
Use nets to represent three-dimensional figures.
Use nets to recognize that the surface area of a prism is equal to the sum of the areas of its faces.
Find the surface area of prisms.
Find the surface area of pyramids.
Investigate the volume of rectangular prisms with fractional edge lengths.
Use formulas to find the volume of rectangular prisms with fractional edge lengths. Evidence of Learning
Formative Assessments: Teacher observations, exit slips, homework, participation, communicator white boards,
Do Nows
Summative/Benchmark Assessment(s): Lesson quizzes
Alternative Assessments: Modified versions of quizzes
Resources/Materials : Smart Board, curriculum folders, scope and sequence calendar, math textbook, math
manipulatives. Online resources such as IXL, xtramath, Think Central, etc
Modifications:
● Special Education Student/504 ‐ Allow errors, Rephrase
questions, directions, and explanations, Allow use of
calculator and extended time on assignments. Consult
IEP/504 for specific modifications/accommodations. ● English Language Learners ‐ Allow errors in speaking,
rephrase questions, directions, and explanations,
extended time on assignments.
● At-Risk Students - Consult with Guidance
Counselors and follow I&RS procedures/action
plans, extra help, breaking down tasks. ● Gifted and Talented Students – Make Peer Leaders,
provide extension activities.
Suggested Pacing Guide Lesson
Name/Topic Lesson Objective(s)
Students will... Time frame (day(s) to complete)
Midland Park Public Schools
Intro to
Geometry
Demonstrate prior knowledge of
polygons
1 day
Area of Polygons Find the area of rectangles, squares
parallelograms, triangles, and
trapezoids.
3 days
Area of Regular
Polygons
Find the area of regular polygons.
1 day
Area of
Composite
Figures
Find the area of composite figures.
2 day
Polygons on the
Coordinate Plane
Plot polygons on a coordinate plane,
and use coordinates to find side lengths.
1 day
Assessment Demonstrate skills above 1 day
Intro to 3D
shapes
Use nets to represent three-dimensional
figures.
2 days
Intro to Surface
Area
Use nets to recognize that the surface
area of a prism is equal to the sum of
the areas of its faces.
1 day
Surface Area of
Prisms
Find the surface area of prisms. 2 days
Surface Area of
Pryamids
Find the surface area of pyramids. 2 days
Volume of
Rectangular
Prisms
Investigate the volume of rectangular
prisms with fractional edge lengths.
2 days
Volume of
Prisms with
Fractional Side
Lengths
Use formulas to find the volume of
rectangular prisms with fractional edge
lengths.
2 days
Assessment Demonstrate skills above 1 day
Teacher Notes: Use Quadrilateral Hierarchy when introducing Geometry. Use Geomodels to draw nets of 3D shapes.
Use paper nets to discover the nets of a cube.
Additional Resources:
https://www.ixl.com/ https://www.khanacademy.org/
https://xtramath.org
https://www-k6.thinkcentral.com/ePC/start.do
Midland Park Public Schools
Unit 5 - Overview Content Area: Mathematics
Unit Title: Unit 5: Statistics and Probability
Grade Level: 6th
Unit Summary
● Measures of Center ● Data Displays
Students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected.
Unit 5 - Standards
Standards (Content and Technology):
CPI#: Statement:
6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and
accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old
are the students in my school?” is a statistical question because one anticipates variability in students’
ages.
6.SP.A.2 Understand that a set of data collected to answer a statistical question has a distribution which can be
described by its center, spread, and overall shape.
6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single
number, while a measure of variation describes how its values vary with a single number.
6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
6.SP.B.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of
observations. b. Describing the nature of the attribute under investigation, including how it was
measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean)
and variability (interquartile range and/or mean absolute deviation), as well as describing any overall
pattern and any striking deviations from the overall pattern with reference to the context in which the
data were gathered. d. Relating the choice of measures of center and variability to the shape of the data
distribution and the context in which the data were gathered.
21st century themes and skills (standard 9)
9.1.8.E.1 Explain what it means to be a responsible consumer and the factors to consider when making consumer
decisions.
Career Ready Practices
CRP1 Act as a responsible and contributing citizen and employee.
CRP2 Apply appropriate academic and technical skills.
CRP4 Communicate clearly and effectively and with reason.
CRP8 Utilize critical thinking to make sense of problems and persevere in solving them.
Educational Technology Standards
8.1.8.A.1 Demonstrate knowledge of a real world problem using digital tools.
8.1.8.A.3 Use and/or develop a simulation that provides an environment to solve a real world problem or theory.
Interdisciplinary Connection
SL.6.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-
led) with diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and
expressing their own clearly. SL.6.2 Interpret information presented in diverse media and formats (e.g., visually, quantitatively, orally) and
explain how it contributes to a topic, text, or issue under study.
NJSLSA.L2 Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling
when writing.
Midland Park Public Schools
Unit Essential Question(s):
How do you divide multi-digit numbers?
How do you identify a statistical question?
How can you describe how a data set was collected?
How can you use dot plots and frequency tables to
display data?
How can you use histograms to display data?
How does the mean represent a fair share and balance
point?
How can you describe a set of data using mean,
median, and mode?
How does an outlier affect measures of center?
How can you describe overall patterns in a data set?
How can you use box plots to display data?
How do you calculate the mean absolute deviation of
a data set?
How can you summarize a data set by using range,
interquartile range, and mean absolute deviation?
How can you choose appropriate measures of center
and variability to describe a data set?
What do measures of center and variability indicate
about a data set?
How can you describe the distribution of a data set
collected to answer a statistical question?
Unit Enduring Understandings:
Finding the mean, median, and mode of a set of
data and discussing which measure is most
appropriate to answer a statistical question
provide students an opportunity to construct
viable arguments and critique the reasoning of
others.
As students work with data, they model with
mathematics through dot plots, histograms, and
box plots. The models reinforce given numerical
information visually and help students analyze
and interpret measures of center and dispersion to
draw conclusions.
Unit Learning Targets/Objectives:
Students will be able to...
Recognize statistical questions.
Describe a data set by stating what quantity was measured and how it was measured.
Use frequency tables and dot plots to organize data.
Display data in histograms.
Understand the mean as a fair share and as a balance point.
Summarize a data set by using mean, median, and mode.
Determine the effects of outliers on measures of center
Describe overall patterns in data, including clusters, peaks, gaps, and symmetry.
Display data in box plots.
Understand mean absolute deviation as a measure of variability from the mean.
Summarize a data set by using range, interquartile range, and mean absolute deviation.
Choose appropriate measures of center and variability to describe data, and justify the choice.
Recognize what measures of center and variability indicate about a data set.
Describe the distribution of a data set collected to answer a statistical question.
Evidence of Learning
Formative Assessments: Teacher observations, Do Now’s exit slips, homework, participation, communicator
white boards
Summative/Benchmark Assessment(s): Lesson quizzes, Unit Test
Alternative Assessments: Modified versions of quizzes and tests
Resources/Materials : Smart Board, curriculum folders, scope and sequence calendar, math textbook, math
manipulatives. Online resources such as IXL, xtramath, Think Central, etc
Modifications:
● Special Education Student/504 ‐ Allow errors, Rephrase
questions, directions, and explanations, Allow use of
calculator and extended time on assignments. Consult
IEP/504 for specific modifications/accommodations.
● At-Risk Students - Consult with Guidance
Counselors and follow I&RS procedures/action
plans, extra help, breaking down tasks.
Midland Park Public Schools
● English Language Learners ‐ Allow errors in speaking,
rephrase questions, directions, and explanations,
extended time on assignments.
● Gifted and Talented Students – Make Peer Leaders,
provide extension activities.
Suggested Pacing Guide Lesson
Name/Topic Lesson Objective(s)
Students will... Time frame (day(s) to complete)
Statistical
Questions Recognize statistical questions.
1 day
Mean, Median,
and Mode
Summarize a data set by using mean,
median, and mode.
Understand the mean as a fair share and
as a balance point.
2 days
Choosing
Measures of
Center
Choose appropriate measures of center
and variability to describe data, and
justify the choice.
2 days
Outliers Determine the effects of outliers on
measures of center.
1 day
Describe Data Describe a data set by stating what
quantity was measured and how it was
measured.
Describe overall patterns in data,
including clusters, peaks, gaps, and
symmetry.
2 days
Dot Plots and
Histograms
Use frequency tables and dot plots to
organize data.
Display data in histograms.
2 days
Box Plots Display data in box plots. 2 days
Mean Absolute
Deviation
Understand mean absolute deviation as
a measure of variability from the mean.
2 days
Summarize Data Summarize a data set by using range,
interquartile range, and mean absolute
deviation.
1 day
Distribution of
Data
Recognize what measures of center and
variability indicate about a data set.
Describe the distribution of a data set
collected to answer a statistical
question.
2 days
Assessment Demonstrate skills above 2 days
Benchmark
Testing
2 days
Teacher Notes: Use chips to find mean as a balance point. Also, use ruler and half paper towel tube to find mean as a
balance point and to help explain mean absolute deviation. Use inch cubes for volume of rectangular prisms.
Additional Resources:
https://www.ixl.com/ https://www.khanacademy.org/
https://xtramath.org
https://www-k6.thinkcentral.com/ePC/start.do